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Didn't log in for a while and just out of curiosity tried the login via email as well. At the first time I tried, nothing happened. 2nd time I got the code in the email, entered it and clicked to confirm and then got back to the starting site without being logged in. 3rd time I didn't get the email. 4th try I got the email again, entered the code and nothing happened, just loading for a couple of seconds and back to the "enter your code" message. At that point unfortunately I had to give up because I didn't see merit in continuing to try. Hope this is getting fixed soon!
Is this a new account that was only created by email address or an old Telegram account?
I've already had problems with disposable email addresses, which didn't work for me either. However, I then created an alias email address via outlook.com and no longer had any problems with this.